Question

Education of Prisoners. Refer to Exercise 12.49.

a. Find the conditional distribution of educational attainment with in each type of prison facility.

b. Does an association exist between educational attainment and of prison facility for prisoners? Explain your answer.

c. Determine the marginal distribution of educational attainment for prisoners.

d. Construct a segmented bar graph for the conditional distributions of educational attainment and marginal distribution of educational attainment that you obtained in parts (a) and (c), respectively. Interpret the graph in light of your answer to part (b).

e. Without doing any further calculations, respond true or false to the following statement and explain your answer: "The conditional distributions of facility type within educational attainment categories are identical."

f. Determine the marginal distribution of facility type and the conditional distributions of facility type within educational attainment

categories.

g. Find the percentage of prisoners who are in federal facilities.

h. Find the percentage of prisoners with at most an 8th-gradetion who are in federal facilities.

i. Find the percentage of prisoners in federal facilities who have at most an 8th-grade education.

Short answer

(a)

ATTAINMENT	State	Federal	Local
8th grade or less	0.142	0.119	0.131
Some HS	0.255	0.145	0.334
GED	0.285	0.226	0.141
HS Diploma	0.205	0.270	0.259
Postsecondary	0.090	0.158	0.103
college grade or more	0.024	0.081	0.032
TOTAL	1	1	1

(b)Yes, there is a link between academic achievement and the type of prisoner because the conditional allocation of institutional type between the stages of education is not the same.

(c)

ATTAINMENT	State	Federal	Local	Marginal distribution
8th grade or less	149.9	10.6	66	0.137
Some HS	269.1	12.9	168.2	0.273
GED	300.8	20.1	71	0.238
HS Diploma	216.4	24	130.4	0.225
Postsecondary	95	14	51.9	0.098
college grade or more	25.3	7.2	16.1	0.029
TOTAL	1056.5	88.8	503.6	1

(d)

(e)Here, the statement given is false because the variables "prison facility and" educational benefits are linked. This means that the conditional distribution of the type of prison institution in the stages of access to education is not the same.

(f)

ATTAINMENT	State	Federal	Local	Marginal distribution
8th grade or less	0.662	0.047	0.291	1
Some HS	0.598	0.029	0.374	1
GED	0.768	0.051	0.181	1
HS Diploma	0.584	0.065	0.352	1
Postsecondary	0.590	0.087	0.323	1
college grade or more	0.521	0.148	0.331	1
TOTAL	1056.5	88.8	0.305	1

(g)5.4% is the percentage.

(h)4.7 % is the percentage

(i)11.9% is the highest 8th grade education.

Step-by-step solution

Step 1. Part ( a ) Find the conditional distribution of educational attainment within each type of prison facility.

ATTAINMENT	State	Federal	Local
8th grade or less	0.142	0.119	0.131
Some HS	0.255	0.145	0.334
GED	0.285	0.226	0.141
HS Diploma	0.205	0.270	0.259
Postsecondary	0.090	0.158	0.103
college grade or more	0.024	0.081	0.032
TOTAL	1	1	1

Step 2. Part ( b ) Examine whether there is a link between educational attainment and the type of prison a place for prisoners or not.

Yes, there is a link between academic achievement and the type of prisoner because the conditional allocation of institutional type between the stages of education is not the same.

Step 3. Part ( c )  Finding the marginal distribution

ATTAINMENT	State	Federal	Local	Marginal distribution
8th grade or less	149.9	10.6	66	0.137
Some HS	269.1	12.9	168.2	0.273
GED	300.8	20.1	71	0.238
HS Diploma	216.4	24	130.4	0.225
Postsecondary	95	14	51.9	0.098
college grade or more	25.3	7.2	16.1	0.029
TOTAL	1056.5	88.8	503.6	1

Step 4. Part ( d ) Construct a bar graph

MINITAB procedure:

Step 1: Select Graph> Bar Chart

Step 2: In the representative bars, select the values in the table

Step 3: Select Stack under the two-way table, then click OK.

Step 4 Graph variables, enter the State Federal and Local column:

Step 5. In the Row labels, select ATTAINMENT

Step 6. Check the columns that are the most out of the columns and the rows are actually the inside

Step 7: Click OK

Step 5. MINITAB Output

Step 6. Part (e) Find if the statement is false or true.

Here, the statement given is false because the variables "prison facility and" educational benefits are linked. This means that the conditional distribution of the type of prison institution in the stages of access to education is not the same.

Step 7. Part (f) Determine the marginal distribution

ATTAINMENT	State	Federal	Local	Marginal distribution
8th grade or less	0.662	0.047	0.291	1
Some HS	0.598	0.029	0.374	1
GED	0.768	0.051	0.181	1
HS Diploma	0.584	0.065	0.352	1
Postsecondary	0.590	0.087	0.323	1
college grade or more	0.521	0.148	0.331	1
TOTAL	1056.5	88.8	0.305	1

Step 8. Part (g) Find the percentage of prisoners who are in federal facilities.

5.4% is the percentage.

Step 9. Part (h) Find the percentage of prisoners with at least 8th grade education in government facilities

4.7 % is the percentage

Step 10. Part (i) Find the percentage of inmates in government institutions with the highest 8th grade education.

11.9% is the highest 8th grade education.